TY - JOUR
T1 - Towards complete detection of unstable periodic orbits in chaotic systems
AU - Davidchack, Ruslan L.
AU - Lai, Ying-Cheng
AU - Klebanoff, Aaron
AU - Bollt, Erik M.
N1 - Funding Information:
We thank Prof. J.A. Yorke for a stimulating discussion motivating us to look into the problem of complete detection of UPOs. R.D. and Y.C.L. are supported by AFOSR under Grant No. F49620-98-1-0400 and by NSF under Grant No. PHY-9996454. A.K. and E.B. are supported by NSF under Grant No. DMS-9704639 and E.B. is supported by NSF Grant No. DMS-0071314.
PY - 2001/8/20
Y1 - 2001/8/20
N2 - We present a rigorous analysis and numerical evidence indicating that a recently developed methodology for detecting unstable periodic orbits is capable of yielding all orbits up to periods limited only by the computer precision. In particular, we argue that an efficient convergence to every periodic orbit can be achieved and the basin of attraction can be made finite and accessible for typical or particularly chosen initial conditions.
AB - We present a rigorous analysis and numerical evidence indicating that a recently developed methodology for detecting unstable periodic orbits is capable of yielding all orbits up to periods limited only by the computer precision. In particular, we argue that an efficient convergence to every periodic orbit can be achieved and the basin of attraction can be made finite and accessible for typical or particularly chosen initial conditions.
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U2 - 10.1016/S0375-9601(01)00463-7
DO - 10.1016/S0375-9601(01)00463-7
M3 - Article
AN - SCOPUS:0035920641
SN - 0375-9601
VL - 287
SP - 99
EP - 104
JO - Physics Letters, Section A: General, Atomic and Solid State Physics
JF - Physics Letters, Section A: General, Atomic and Solid State Physics
IS - 1-2
ER -